My 'reality-based decision making' post prompted a comment asking for my thoughts about sea level rise, which is more than sufficient excuse to turn to that. An additional excuse is that it provides a chance to look at how to decide climate time scales for something other than temperatures. For global mean temperature trends, I found that you need 20-30 years to determine a climate trend. We'll see that it is 40-60 years, 60 for preference, for sea level.
My starting point for data was the University of Colorado sea level group. They provide satellite data back to late 1992. High quality data, but only for a short period of time. If global sea level's time scales are like global mean temperature's, then it's only just gotten long enough to provide a climate number. Fortunately they list links to other sea level groups, including the Permanent Service for Mean Sea Level. They have three global reconstructions available. I'll take this one -- published in the scientific literature as: Recent global sea level acceleration started over 200 years ago?", Jevrejeva, S., J. C. Moore, A. Grinsted, and P. L. Woodworth (2008), Geophys. Res. Lett., 35, L08715, doi:10.1029/2008GL033611 -- on the grounds that it covers the longest time period and has the most recent literature publication date. It will be a good project for a reader to see if the conclusions here change, and how, if you use one of the others instead.
My starting point with any data is, plot it and start to get a sense of what we're looking at. This includes not to draw lines between data points, as the lines can mislead me as to what's going on. Try it some time. The lines typically make the data look much smoother than they do if you leave them off. That's not always a help, as it can push you to thinking that you have a significant relationship that you don't. Anyhow, the first plot of the 300 years of data is:
Two things seem obvious from this figure. First, the data before about 1880 have a lot more scatter than the more recent data. Second, the change in sea level is markedly more rapid in the more recent half than the first half. Read the paper for the discussion of the change in rise, how confident you can be that it's truly different and not just a matter of noisy data, and so forth.
For our purposes, I'll start with 1880, same as the NCDC global temperature record, and look from there for the climate time scale on sea level. The straightforward plot of the data is now:
cumulative sums, where Tamino observed at his blog that there are distinct problems with using cumulative sums. I didn't/don't think that his concerns truly applied to my application then, and you can follow that up in some update articles I wrote later (links in updates at the end of the article.) But here ... I'm more concerned about those issues.
Sea level is the cumulative sum of changes in sea level. When you get to calculus, you'll find the term is sea level is the integral of sea level change, or, equally, sea level change is the first derivative of sea level itself. Physically, we're not so much concerned with sea level itself, at least in the sense of how many meters from the top of the ocean to the center of the earth. We're more concerned with the change -- if sea level gets to be higher than it used to be, it can drown ports, amplify flooding from storm surge, and so forth. As we eyeball the data above, we see that there's a strong general trend towards higher sea level. On the other hand, if we look very closely, we see that there are some large changes year to year above and below the main body of the trend.
Since, again, eyeballs can be fooled, let's do the more direct thing and compute how much sea level changed from one year to the next and plot that:
I'll return, though, to my simple approach of looking for a time period around which the estimates of trend don't change much as you change the length of the period. Below are figures for trends ending in 2002, starting from the noted year (working with the whole time series now, not just the recent segment), and for trends ending in 1940 (from 1700-1939) or starting from 1940 (ending in the noted year).
It's no challenge to see that within 20 years of the year we reference, the trends are wildly variable and sensitive to just how long a time period you take. So anything less than 20 years needs some much more sophisticated analysis methods than I'm using on this blog. (You'll see some examples of what more sophisticated means when you hit the scientific literature.) To get some more or less consistent trend estimates, you need 40-60 years of global sea level data. 60 for preference, according pretty well, even though it didn't have to, with the estimate above from mean vs. standard deviation.
In some of my fooling around with the data, there was some eyeball suggestion of a 60-ish year cycle in sea level change. That encouraged me to look to the scientific literature for whether a 60-ish year cycle has been noticed as a possibility already. The answer is yes, and it appears to be even more complex than this simple analysis would suggest. See Is there a 60 year oscillation in global mean sea level?, also at the University of Colorado sea level group's page.
If there's a strong possibility of 60 year cycle in the data, then you definitely want to average over the 60 years. My simple fooling around with it suggested that the magnitude of the cycle is about 20 mm, with recent years having been at the bottom of the cycle. That would suggest that using only simple analysis of the data for recent years would be leading to sizeable underestimates of sea level rates of change. As the scientific literature is already suggesting the rate of sea level rise has been increasing, that's not comforting news.
So, where are we? Well, on one hand, it suggests that trying to understand sea level change only by looking at data is a much more difficult matter than looking at global mean surface air temperatures is. Not least, that you need 60ish years of data to establish a 'climate' in sea level, while temperature can be done in 20-30 years. On the second hand, the large variability in year to year sea level change says that there are very large sources and sinks for water that can operate for a year or two (or several). "What are they exactly?" On another hand, it says that there must be something interesting to learn about the climate system -- "Why is sea level change so variable as compared to surface air temperature?
Therefore ... more posts will be coming on sea level. I was quite surprised by the year to year variability in sea level.
* 'exercise for the reader' is notorious textbook-speak for "this can be done, but it'll take a lot of time and be more involved than I feel like doing here". If you know your college intro. to statistics material, the math I'm referring to is obvious. If you don't, it'll take a fair amount of time to explain it.
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